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A006960
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Reverse and Add! sequence starting with 196.
(Formerly M5410)
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32
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196, 887, 1675, 7436, 13783, 52514, 94039, 187088, 1067869, 10755470, 18211171, 35322452, 60744805, 111589511, 227574622, 454050344, 897100798, 1794102596, 8746117567, 16403234045, 70446464506, 130992928913, 450822227944, 900544455998, 1800098901007
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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a(1) = 196; a(n+1) = a(n) + a(n)-with-digits-reversed.
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 196, p. 58, Ellipses, Paris 2008.
Martianus Frederic Ezerman, Bertrand Meyer and Patrick Sole, On Polynomial Pairs of Integers, arXiv http://arxiv.org/abs/1210.7593. 2012. - From N. J. A. Sloane, Nov 08 2012
F. Gruenberger, Computer Recreations, Scientific American, 250 (No. 4, 1984), 19-26.
R. K. Guy, What's left?, preprint, 1998.
D. H. Lehmer, "Sujets d'etude. No. 74," Sphinx (Bruxelles), 8 (1938), 12-13. (This is the currently earliest known reference to the 196 Problem). - James D. Klein, Apr 09 2012.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 70.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe and Michael Lee, Table of n, a(n) for n = 0..2390 (T. D. Noe supplied terms 0 to 200)
P. De Geest, Some thematic websources
Jason Doucette, World Records
T. Irvin, About Two Months of Computing, or An Addendum to Mr. Walker's Three Years of Computing
Madras Math's Amazing Number Facts, The Ultimate Palindrome
I. Peter, More trajectories
Wade VanLandingham, 196
J. Walker, Three Years Of Computing: Final Report On The Palindrome Quest
Eric Weisstein's World of Mathematics, 196-Algorithm.
Eric Weisstein's World of Mathematics, Palindromic Number Conjecture.
Index entries for sequences related to Reverse and Add!
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MATHEMATICA
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a = {196}; For[i = 2, i < 26, i++, a = Append[a, a[[i - 1]] + ToExpression[ StringReverse[ToString[a[[i - 1]]]]]]]; a
NestList[#+FromDigits[Reverse[IntegerDigits[#]]]&, 196, 25] (* From Harvey P. Dale, June 05 2011 *)
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PROG
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(Haskell)
a006960 n = a006960_list !! n
a006960_list = iterate a056964 196 -- Reinhard Zumkeller, Sep 22 2011
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CROSSREFS
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Cf. A023108, A023109, A033665, A016016, A056964, A004086.
Sequence in context: A089493 A088753 A063048 * A014798 A178722 A061622
Adjacent sequences: A006957 A006958 A006959 * A006961 A006962 A006963
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KEYWORD
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nonn,base,nice,easy
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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EXTENSIONS
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196 is conjectured to be smallest initial term which does not lead to a palindrome. John Walker, Tim Irvin and others have extended the trajectory of 196 to millions of digits without finding a palindrome.
More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 28 2002
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STATUS
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approved
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